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Use the expansion of (x – 0.2)5 to find the exact value of 9.85
(Solved)
Use the expansion of (x – 0.2)5 to find the exact value of 9.85
Date posted:
June 20, 2019
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Answers (1)
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Solve for x in the equation;
log (x + 24) = 2 log 3 + log (9 – 2x).
(Solved)
Solve for x in the equation;
log (x + 24) = 2 log 3 + log (9 – 2x).
Date posted:
June 20, 2019
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Answers (1)
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a) Using binomial expansion, determine the first five terms of the expansion: (2-1/x)8
b) Use the expansion above to evaluate (1.75)8
(Solved)
a) Using binomial expansion, determine the first five terms of the expansion: (2-1/x)8
b) Use the expansion above to evaluate (1.75)8
Date posted:
June 20, 2019
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Answers (1)
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The figure O and P are centres of two intersecting circles. ABE is tangent to circle BCD
at B angle BCD is 42o
(a) Giving reasons for...
(Solved)
The figure O and P are centres of two intersecting circles. ABE is tangent to circle BCD
at B angle BCD is 42o
(a) Giving reasons for your answer, find:-
(i) CBD
(ii) DOB
(iii) DAB
(iv) CDA
b) Show that ADB is isosceles
Date posted:
June 20, 2019
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Answers (1)
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The figure below shows two intersecting circles radii 8 cm and 6 cm respectively.
The common chord AB = 9cm ad P and Q are the...
(Solved)
The figure below shows two intersecting circles radii 8 cm and 6 cm respectively.
The common chord AB = 9cm ad P and Q are the centres as shown:
(a) Calculate the size of angles:-
(i) APB
(ii) AQB
(b) Calculate the area of the shaded region
Date posted:
June 19, 2019
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Answers (1)
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In the figure below ABC is a tangent to the circle at B. given that
(Solved)
In the figure below ABC is a tangent to the circle at B. given that 
Find the sizes of the following angles giving reasons in each case:
a)BDG
b)DGE
c)EFG
d)CBD
e)BCD
Date posted:
June 19, 2019
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Answers (1)
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The figure below shows a circle centre O. AB and PQ are chords intersecting externally
at a point C. AB = 9cm, PQ = 5cm and...
(Solved)
The figure below shows a circle centre O. AB and PQ are chords intersecting externally
at a point C. AB = 9cm, PQ = 5cm and QC = 4cm. Find the value of x
Date posted:
June 19, 2019
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Answers (1)
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Two pipes A and B can fill a tank in 3hrs and 4 hrs respectively. Pipe C can empty the full tank
in 6 hrs.
i) How...
(Solved)
Two pipes A and B can fill a tank in 3hrs and 4 hrs respectively. Pipe C can empty the full tank
in 6 hrs.
i) How long would it take pipes A and B to fill the tank if pipe C is closed?
ii) Starting with an empty tank, how long would it take to fill the tank with all pipes running?
Date posted:
June 19, 2019
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Answers (1)
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The figure below shows two pulleys of radii 6cm and 4cm with centres A and B respectively.
AB = 8cm. The pulleys are connected by a...
(Solved)
The figure below shows two pulleys of radii 6cm and 4cm with centres A and B respectively.
AB = 8cm. The pulleys are connected by a string PQXRSY
Calculate:
(a) Length PQ
(b) PAS reflex
(c) Length of arc PYS and QXR
(d) The total length of the string PQXRSY
Date posted:
June 19, 2019
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Answers (1)
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In the figure below angle BAC =52o, angle ACB = 40o and AD = DC. The radius of
the circle is 7cm. EF is a tangent...
(Solved)
In the figure below angle BAC =52o, angle ACB = 40o and AD = DC. The radius of
the circle is 7cm. EF is a tangent to the circle
(a) Find; giving reasons
(i) angle DCF
(ii) angle AOB (obtuse)
(b) Calculate the area of the shaded segment AGB
Date posted:
June 19, 2019
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Answers (1)
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The figure below shows two circles centres A and B and radii 6 cm and 8 cm respectively. The
circles intersect at P and Q. Angle...
(Solved)
The figure below shows two circles centres A and B and radii 6 cm and 8 cm respectively. The
circles intersect at P and Q. Angle PAB = 420 and angle ABQ = 300.
(a) Find the size of ∠PAQ and PBQ.
(b) Calculate, to one decimal place the area of:
(i) Sector APQ and PBQ.
(ii) Triangle APQ and PBQ.
(iii) The shaded area (take π 22)
Date posted:
June 19, 2019
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Answers (1)
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A customer deposited Ksh.15,500 in a savings account. Find the accumulated amount
after 3½ years if interest was paid at 16% per annum compounded semi-annually
(Solved)
A customer deposited Ksh.15,500 in a savings account. Find the accumulated amount
after 3½ years if interest was paid at 16% per annum compounded semi-annually
Date posted:
June 19, 2019
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Answers (1)
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The table below shows the annual income tax rates for a certain year.
Kiptoo earns a monthly salary of Kshs.25000. He is entitled to house and...
(Solved)
The table below shows the annual income tax rates for a certain year.
Kiptoo earns a monthly salary of Kshs.25000. He is entitled to house and medical allowances
of Kshs.12000 and Kshs.3000 respectively
Calculate:
(a) His taxable income per month
(b) His monthly tax payable
(c)His annual tax payable
Date posted:
June 19, 2019
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Answers (1)
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A company employee earns a basic salary of Kshs.25,000 and is also given taxable allowances
amounting to Kshs.10,480.
Using the table of taxation above:-
(a) Calculate the employee’s...
(Solved)
A company employee earns a basic salary of Kshs.25,000 and is also given taxable allowances
amounting to Kshs.10,480.
Using the table of taxation above:-
(a) Calculate the employee’s taxable income
(b) If the employee is entitled to a personal tax relief of Kshs.800 per month, determine the net tax
(c) If the employee was given 40% increase in his income, calculate the percentage increase
in his income tax
Date posted:
June 19, 2019
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Answers (1)
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A certain amount of money was invested at compound interest of 10% compounded
every two years for ten years. Given that the investor invested a total...
(Solved)
A certain amount of money was invested at compound interest of 10% compounded
every two years for ten years. Given that the investor invested a total of 500,000/= at the
end of the ten years, find the amount of money invested to the nearest shillings
Date posted:
June 19, 2019
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Answers (1)
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The cash price of a T.V set is Ksh. 26,000. Linda bought the set on hire purchase terms by
paying a deposit of Ksh. 6,000 and...
(Solved)
The cash price of a T.V set is Ksh. 26,000. Linda bought the set on hire purchase terms by
paying a deposit of Ksh. 6,000 and the balance by 24 equal monthly installments of
Khs. 1,045.30. Find the compound rate of interest per year.
Date posted:
June 19, 2019
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Answers (1)
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What would Kshs.15000 amount to after 3years at 16% per annum compounded quarterly?
(Solved)
What would Kshs.15000 amount to after 3years at 16% per annum compounded quarterly?
Date posted:
June 19, 2019
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Answers (1)
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Income rates for income earned were charged as follows:
Income in Kshs. p.m Rate in Kshs. per sh.20
1- 8400 ...
(Solved)
Income rates for income earned were charged as follows:
Income in Kshs. p.m Rate in Kshs. per sh.20
1- 8400 2
8401- 18,000 3
18,001- 30,000 4
30,000 - 36,000 5
36,001 - 48,000 6
48,001 and above 7
A civil servant earns a monthly salary of Ksh.19,200. His house allowance is Ksh12,000 per
month. Other allowces per month are transport Ksh.1300 and medical allowance Ksh.2300.
He is entitled to a family relief of Kshs. 1240 per month.
Determine:
a) (i) His taxable income per month.
(ii) Net tax. b) In addition, the following deductions were made
NHIF shs. 230
Service charge Kshs. 100
Loan repayment Kshs. 4000
Co-operative shares of Kshs. 1200.
Calculate his net salary per month.
Date posted:
June 19, 2019
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Answers (1)
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Use the taxation rates in the table below to answer the questions that follow;-
The manager of a certain company is entitled to a monthly personal...
(Solved)
Use the taxation rates in the table below to answer the questions that follow;-
The manager of a certain company is entitled to a monthly personal relief of shs.3000
and her tax (PAYE) is kshs.9000 per month she is also deducted NHIF shs.350 per month,
WCPS shs.800 per month and cooperative shares shs.1200 per month, calculate
(a) The managers total deductions per month
(b) Total tax per month
(c) The manager’s annual gross salary
(d) The manager’s monthly basic salary if her monthly allowance and medical allowances
are 10000 and 2000 shillings
Date posted:
June 19, 2019
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Answers (1)
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The table below shows the income tax for a certain year;
In that year, Odero paid a net tax of Kshs.5,512 per month. His total monthly...
(Solved)
The table below shows the income tax for a certain year;
In that year, Odero paid a net tax of Kshs.5,512 per month. His total monthly taxable allowances
amounted to Kshs.15,220 and he was entitled to a monthly personal relief of kshs.1,162.
Every month the following deductions were made;
N.H.I.F Kshs.320
Union dues Kshs.200
Co-operative shares Kshs.7,500
(a) Calculate Odero’s monthly basic salary in Kshs
(b) Calculate his monthly salary
Date posted:
June 19, 2019
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Answers (1)